Explanation of 44.1 kHz CD sampling rate

The CD sampling rate has to be larger than about 40 kHz to fulfill
the Nyquist criterion that requires sampling at twice the maximum analog
frequency, which is about 20 kHz for audio. The sampling frequency is
chosen somewhat higher than the Nyquist rate since practical filters
neede to prevent aliasing have a finite slope. Digital audio tapes
(DATs) use a sampling rate of 48 kHz. It has been claimed that thier
sampling rate differs from that of CDs to make digital copying from one
to the other more difficult. 48 kHz is, in principle, a better rate
since it is a multiple of the other standard sampling rates, namely 8
and 16 kHz for telephone-quality audio. Sampling rate conversion is
simplified if rates are integer multiples of each other.

From John Watkinson, The Art of Digital Audio, 2nd edition,
pg. 104:

In the early days of digital audio research, the necessary bandwidth
of about 1 Mbps per audio channel was difficult to store. Disk drives
had the bandwidth but not the capacity for long recording time, so
attention turned to video recorders. These were adapted to store
audio samples by creating a pseudo-video waveform which would convey
binary as black and white levels. The sampling rate of such a system
is constrained to relate simply to the field rate and field structure
of the television standard used, so that an integer number of samples
can be stored on each usable TV line in the field. Such a recording
can be made on a monochrome recorder, and these recording are made in
two standards, 525 lines at 60 Hz and 625 lines at 50 Hz. Thus it is
possible to find a frequency which is a common multiple of the two and
is also suitable for use as a sampling rate.

The allowable sampling rates in a pseudo-video system can be deduced
by multiplying the field rate by the number of active lines in a field
(blanking lines cannot be used) and again by the number of samples in
a line. By careful choice of parameters it is possible to use either
525/60 or 625/50 video with a sampling rate of 44.1KHz.

In 60 Hz video, there are 35 blanked lines, leaving 490 lines per
frame or 245 lines per field, so the sampling rate is given by :

60 X 245 X 3 = 44.1 KHz

In 50 Hz video, there are 37 lines of blanking, leaving 588 active
lines per frame, or 294 per field, so the same sampling rate is given
by

50 X 294 X3 = 44.1 Khz.

The sampling rate of 44.1 KHz came to be that of the Compact Disc.
Even though CD has no video circuitry, the equipment used to make CD
masters is video based and determines the sampling rate.

(Reference kindly provided by Kavitha Parthasarathy.)

Also, David Singer noted that 44,100 can be factored as 2^2 * 3^2 *
5^2 * 7^2, i.e., the product of the squares of the first four prime
numbers.